Density of what exactly? The event horizon? But that's not a "real" thing, it's merely a limit where things happen. Density of the central singularity? In what time frame? Also, current science gives you an infinite result for that one, meaning the theory is incomplete. There are no good answers here, because the question doesn't make a whole lot of sense.
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Florin AndreiMar 15 '12 at 15:20

4 Answers
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Black holes are really hard to get a density. Basically, they are so dense that there is no known mechanism for providing sufficient outward force to counterbalance the inward pull of gravity, so they will collapse into an infinitesimally small size. Of course, that doesn't seem likely, it seems likely there is something that will keep the volume from being 0, but it is extremely dense.

An alternative method of measuring the volume of a black hole is to take the radius beyond which light can't escape, also commonly known as the Event horizon. Wikipedia has a great article on potential black hole sizes and masses, using the event horizon. Here's a few example values:

It helps to specify that you're talking about the mean density of the black hole. Like you say, it doesn't really make sense to talk about the "actual" density because (a) GR implies collapse to a point of infinite density and (b) we don't have a quantum theory to replace GR, although that might describe what actually happens. And the mean density can still be helpful.
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WarrickMar 15 '12 at 8:08

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@Warrick: GR doesn't imply collapse to a point of infinite density, it implies an end for the infalling matter in the symmetric nonrotating collapse case. The singularity is not a spatial point of infinite density, it is a terminus for the infalling geodesics. The only meaning to a black hole density is the ratio of mass to the cube of the Schwarzschild radius.
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Ron MaimonNov 2 '12 at 17:25

What are you using for the volume here? The result you get depends on what spatial section you choose to measure. And a natural choice $\frac{4}{3}\pi r_s^3$ (for Schwarzschild radius $r_s$) isn't really the volume of anything.
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HolographerMay 13 at 14:04

We can't tell how matter behaves inside a black hole. I can think of at least several solutions, but there is no way to either confirm or deny them.

I'd say its most likely matter forms a sphere inside the event horizon equal to the radii of the black hole. Considering physics (as we know it) don't break down inside the black hole, matter can't travel faster than c and time is infinitely extended.

A black hole is a celestial body of extreme density and high gravitational pull that not reflect or emit radiation.

The process of forming a black hole is related to the evolution of some stars. As you know, a star of similar mass to the Sun ends up becoming a white dwarf, a small star with high density.

The explosion of a nova leaves behind a new star of enormous density and small volume with a diameter not exceeding 10 km., Consisting solely of neutrons.

moreover, the density of a black hole should not be the same for all, because each has a different size depending on the original mass of the collapsed star. but that there should be no doubt that this density is very high.

There might be no full-fledged theory of quantum gravity, but we can speculate a little on results from whatever the true theory is. Quantizing gravity usually implies quantizing spacetime- in other words, the entire universe is grainy. It is likely that you can pack no more than about one Planck mass into each Planck volume, i.e. cubic Planck length. This works out to 5.1555e96 kg/m^3. The implication of this calculation is that all black holes will have roughly the same density, and will simply increase in real volume with increasing mass.

I know I've mentioned this on another question, but I can't find it right now.